时空非对易性中氢原子的光谱
Spectrum of Hydrogen Atom in Space-Time Non-Commutativity
摘要：
我们研究了时空非对易性应用于氢原子及其唯象效应。我们发现，它修改的潜在的一部分，以这样的方式，我们得到的Kratzer势，而不是库仑之一，这是类似于添加一个偶极电位或考虑扩展带电性质的质子在核中。通过解析计算薛定谔方程的能量和微扰理论计算精细结构修正，我们研究了氢原子光谱的修正。我们发现它消除了关于轨道量子数l和总角动量量子数j的简并;它在这里的作用类似于兰姆位移。将计算结果与光谱实验值进行比较，得到了时空非对易参数的一个新的上界。我们对相对论情况做同样的微扰计算，计算狄拉克能量的修正;我们发现，在这种情况下，修正也类似于兰姆位移，它们消除了关于j的简并;我们得到了非对易参数的另一个界。
英文摘要：
We study space-time noncommutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the potential part of the Hamiltonian in such a way we get the Kratzer potential instead of the Coulomb one and this is similar to add a dipole potential or to consider the extended charged nature of the proton in the nucleus. By calculating the energies from the Schrödinger equation analytically and computing the fine structure corrections using perturbation theory, we study the modifications of the hydrogen spectrum. We find that it removes the degeneracy with respect to both the orbital quantum number l and the total angular momentum quantum number j; it acts here like a Lamb shift. Comparing the results with the experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. We do the same perturbative calculation for the relativistic case and compute the corrections of the Dirac energies; we find that in this case too, the corrections are similar to a Lamb shift and they remove the degeneracy with respect to j ; we get an other bound for the parameter of non-commutativity.
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